Is it 'once in their lifetimes' or 'once in their lifetime'?
Either one. There is no possibility of confusion. I would probably use the plural since everyone has a slightly varying length of time on this planet, compared to siimilar constructions, but neither choice is wrong.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.